Semi-Infinite Optimization with Implicit Functions
Author(s)
Stuber, Matthew D.; Barton, Paul I
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In this work, equality-constrained bilevel optimization problems, arising from engineering design, economics, and operations research problems, are reformulated as an equivalent semi-infinite program (SIP) with implicit functions embedded, which are defined by the original equality constraints that model the system. Using recently developed theoretical tools for bounding implicit functions, a recently developed algorithm for global optimization of implicit functions, and a recently developed algorithm for solving standard SIPs with explicit functions to global optimality, a method for solving SIPs with implicit functions embedded is presented. The method is guaranteed to converge to ε-optimality infinitely many iterations given the existence of a Slater point arbitrarily close to a minimizer. Besides the Slater point assumption, it is assumed only that the functions are continuous and factorable and that the model equations are once continuously differentiable.
Date issued
2014-12Department
Massachusetts Institute of Technology. Process Systems Engineering LaboratoryJournal
Industrial & Engineering Chemistry Research
Publisher
American Chemical Society (ACS)
Citation
Stuber, Matthew D., and Paul I. Barton. "Semi-Infinite Optimization with Implicit Functions." Industrial & Engineering Chemistry Research 54, 1 (January 2015), 54: 307−317 © 2014 American Chemical Society
Version: Author's final manuscript
ISSN
0888-5885
1520-5045